Question

tính A=\(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\)

Answer 1

\(A=\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}=\sqrt{\left(4+\sqrt{8}\right)^2}-\sqrt{\left(4-\sqrt{8}\right)^2}=\left|4+\sqrt{8}\right|-\left|4-\sqrt{8}\right|=4+\sqrt{8}-4+\sqrt{8}=4\sqrt{2}\)

Answer 2

\(A=\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\)

\(=\sqrt{8+2.4.2\sqrt{2}+16}-\sqrt{16-2.4.2\sqrt{2}+8}\)

\(=\sqrt{\left(2\sqrt{2}+4\right)^2}-\sqrt{\left(4-2\sqrt{2}\right)^2}\)

\(=2\sqrt{2}+4-4+2\sqrt{2}\)

\(=4\sqrt{2}\)